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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 98r, page id 00068199:0195
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pans e
Vedendinam non liceas
e
in Mathesi, ubi continnitatis lex valet, non spernendum
ad detegenda difficilia videtur remedium, ut generalius aliquid
quaeramas,q quod in quaesitum Casus peciati evanescat
si modo ipsum generale set tractabilibes. Exemplo causa quaecilur
terminatio veriei X
seriei convegentis legem esse X
e
X
rus rxy
atus
B= Ixy V- ZXy
pl
xty
U
Frugamus
7
Hoc posito in casu convergendi fiet 1xy = 2∞ 2X y(, X ty) + b
seu XG (DXX yy  2 XF 2xybX
= Xy XX + 2x yXV  xyyq
et fore
G
2x9by + bb XXtbbgy 26
Jam in hoc casu x=y
2 Cx 4 2xb 4 2xb +bbxx (2x, 1ta fore
 2b Haec quidem lex possibilis est, quia cum
X = y etiam sit Z = v
sed videamus an liceat facere
N = 2a- b xy (: iX+y) Nam ita in casu a =b recidit in hanc
sit jam x = y et 2xy (3a - b, : a) Xy (, X + y) = Xy+ a b fi et
(3a = b, : a)   X (:2) = +X + a - b seu 3aX - bX = f2x +2a-2ba
seu x = (3 +1) a 2a4 - 2ba, :, (34) (3+2) a - b
si hoc casu cum a pervenit ad ae b=a, evanescant omnia
si series esset
Xty
e
v
2Xy
+y
terminabio serci foret S2XG =X 2
Quia ZV = xy  hgeralitur EXy = bb
hZ. X. Exy et v = 2X9(i X+y) fiet 2Z =Xy ergo y = ZZ. X
et XV+ yV = 2Xy adeoque y = XV: 2X - V. Et fiet ZZ = XX
94
2XZZ - VZZ = XXV seu XX -22 + ==
l
qe
VN
seu X = Z2 + Z1 (2Z- v0) et y -
VZ
in
Le
Z + Y (2Z- vV)
ivenire eodem modo formatum ex xG et v uli ex xet yus
revera est seremex relativa in qua sequens pendet
in
ex antecedentis mutare in absolutam, seu relationem
quae est inter oidinatam et abscissam, quasi X esse t ordinatias
y abscissa